Determine if the triangles are similar.

A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar

L x W x D cubic yards is the maximum amount of water the pool can contain.

Volume = Length x Width x Depth

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Many forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to calculate the volume for each of these shapes.

from the question:

We need to know the pool's dimensions in order to calculate how much water it can store. Assume the pool has the following dimensions: L yards in length, W yards in breadth, and D yards in depth.

The following formula can be used to determine the pool's volume:

Volume = length, width, and depth

Volume = L, W, and D cubic yards.

The pool may therefore hold a maximum volume of water that is L x W x D cubic yards.

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The maximum amount of water that the pool can contain is the volume of the pool = L x W x D cubic yards.

The volume of a closed surface or object is a three-dimensional mathematical measurement. Cubic volume metrics include m3, cm3, in3, etc.

Any three-dimensional solid's volume is the area it takes up.

Forms come in a wide range of volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylinders, cones, and more. In this lesson, we'll learn how to determine the volume of each of these forms.

Here we need to know the pool's dimensions in order to calculate how much water it can store.

Let the pool's length be L yards.

Let the pool's breadth be W yards.

Let the pool's depth be D yards.

The following formula can be used to determine the pool's volume:

Volume = length × width × depth

⇒ Volume = L × W × D cubic yards.

The pool may therefore hold a maximum volume of water that is:

L x W x D cubic yards.

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The equation for the line that passes through the point (3,−2) , and that is perpendicular to the line with the equation x=2, is given by y = -2

To find the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2, we need to find the slope of the perpendicular line and use the point-slope form of an equation.

The slope of the line x = 2 is undefined, since it is a vertical line. A line that is perpendicular to a vertical line is a horizontal line, and the slope of a horizontal line is 0.

Using the point-slope form of an equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can plug in the values for the slope and the point:

y - (-2) = 0(x - 3)

Simplifying the equation, we get:

y + 2 = 0

y = -2

So the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2 is y = -2. This is a horizontal line that passes through the y-axis at -2.

Answer: y = -2

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The baker needs a total of 3 hours to decorate 4 1/2 cakes.

To decorate one cake, the baker needs 2/3 hour.

To find out how long it takes to decorate 4 1/2 cakes, we need to multiply the time for one cake by 4 1/2 i.e. 9/2

Time for 4 1/2 cakes = (2/3) x (9/2)

When the products are evaluated, we have

Time for 4 1/2 cakes = 3

So, the time taken is 3 hours

Therefore, the baker needs a total of 3 hours to decorate 4 1/2 cakes.

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Completing the table to show the total cost of uniforms with tax, for groups of students from the four states is as follows:

State              Number     Total Cost

                  of Students    (After-tax)

Idaho                     10        $1,431.00

Mississippi             5          $722.25

Hawaii                  15        $2,106.00

Wisconsin             8          $1,134.00.

The total cost for each group of students from the four states can be determined by multiplication.

The multiplication operation for each group or state first computes the total cost before tax and the total cost after tax.

The total cost after tax uses the sales tax factor or rate to multiply the total cost before tax.

Generally, sales taxes are levied by state and local governments to check the consumption and production of certain items and to increase the revenue of the government.

The price before state sales tax of each uniform = $135

Relevant Taxes and Number of Students:

State           Number of Students     Sales Tax Rate

Idaho                     10                                 6%

Mississippi             5                                  7%

Hawaii                  15                                  4%

Wisconsin             8                                  5%

State              Number      Total Cost     Total Cost

                  of Students    (Before tax)    (After-tax)

Idaho                     10        $1,350            $1,431.00 ($135 x 10 x 1.06)

Mississippi             5           $675             $722.25 ($135 x 5 x 1.07)

Hawaii                  15        $2,025          $2,106.00 ($135 x 15 x 1.04)

Wisconsin             8         $1,080            $1,134.00 ($135 x 8 x 1.05)

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As a result, the circle's precise size is (529/4)π³  square centimetres.

A circle is a closed, two-dimensional shape where every point in the surface is equally spaced from a central point. The line of mirror symmetry is formed by all lines that traverse the circle. Additionally, every point has circular symmetry around the centre.

The circumference of a circle is given by the formula:

C = 2πr

where r is the radius of the circle. We can rearrange this formula to solve for the radius:

r = C / 2π

When we substitute the circumference's specified number, we obtain:

r = (23r) / (2π)

Simplifying:

r = (23/2)π

Now that we know the radius, we can use the formula for the area of a circle:

A = πr²

Substituting the value we found for the radius, we get:

A = π[(23/2)π]²

Simplifying:

A = π(529/4)π²

A = (529/4)π³

Therefore, the exact area of the circle is (529/4)π³ square cm.

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The values of 'x' in |3x + 4| > 6, is, x > 3/2 or x < - 10/3.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

We know, If |x| > a, Then x > a or x < - a.

Given, |3x + 4| > 6.

Therefore,

3x + 4 > 6 or 3x + 4 < - 6.

3x > 2 or 3x < - 10.

x > 3/2 or x < - 10/3.

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The statement that √s^2 is equals to the value of s is false, as s² is an even function, hence √s^2 can be equal either to the value of s or to -s.

The s² function is even, hence, for example:

sqrt[(-3)²] = sqrt(9) = 3.

Which proves by contradiction that the statement is false.

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Answer: 5

Step-by-step explanation:

To solve 4/5x + 3 = 7 for x, we must isolate x on one side of the problem.

To begin, remove 3 from both sides to get:

4/5x = 4

Hence, we can multiply both sides by 5/4 to isolate x:

x = 5

As a result, the answer to the equation 4/5x + 3 = 7 is x = 5.

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Answer:

Step-by-step explanation:

I don't know if this is right but i'm just trying to help you. So I did 27 times 9 because the blue part is 9cm and the pink part H is 27cm, I got 243. Then the whole thing is 243cm but you see how it says in blue area=30cm well that means that that small peace if 30cm out of the whole 243cm, so what I did was i subtracted 243cm by 30cm and I got a answer of 213 cm. If that was what you had needed help on. I hope i helped you even a little bit, please let me know if i did help you. And also um i don't know how to friend someone so if you can tell me how to friend someone i was thinking about friending you. And ill also just you some points if you want, say mabey like 10 or 20 points. Thanks and hoped that helped and good luck buddy. :)

Answer:

10 cm

Step-by-step explanation:

The volume of a cylinder is:

V = πr²h

Plug in the known values:

1884 cm³ = 3.14 × r² × 6 cm

Solve for r²:

r² = (1884 cm³)/(3.14 × 6 cm)

r² = 100 cm²

Solve for r:

r = √(100 cm²)

r = 10 cm

This expression will generate all angles coterminal with 240 degrees.

To convert an angle from degrees to degrees, minutes, and seconds, we need to use the following formulas:
1 degree = 60 minutes
1 minute = 60 seconds

First, we need to convert the decimal part of the angle to minutes:
0.32 degrees * 60 minutes/degree = 19.2 minutes

Next, we need to convert the decimal part of the minutes to seconds:
0.2 minutes * 60 seconds/minute = 12 seconds

So, the angle 124.32 degrees is equal to 124 degrees, 19 minutes, and 12 seconds:
124.32 ∘ = 124 ∘ 19 ′ 12 ′′

To convert an angle from degrees, minutes, and seconds to decimal degrees, we need to use the following formulas:
1 degree = 60 minutes
1 minute = 60 seconds

First, we need to convert the minutes to degrees:
36 minutes / 60 minutes/degree = 0.6 degrees

Next, we need to convert the seconds to degrees:
36 seconds / 3600 seconds/degree = 0.01 degrees

So, the angle 48 degrees, 36 minutes, and 36 seconds is equal to 48.61 degrees:
48 ∘ 36 ′ 36 ′′ = 48.61 ∘

To find the angle of least positive measure that is coterminal with a given angle, we need to use the formula:
A = A + 360n

Where A is the given angle, and n is an integer. We need to find the smallest positive value of n that makes the expression equal to a positive angle less than 360 degrees.

For the given angle A = 725 degrees, we can use n = -2:
A = 725 + 360(-2) = 725 - 720 = 5 degrees

So, the angle of least positive measure that is coterminal with 725 degrees is 5 degrees.

To find an expression that generates all angles coterminal with a given angle, we can use the formula:
A = A + 360n

Where A is the given angle, and n is an integer. For the given angle A = 240 degrees, the expression is:
240 ∘ + 360n

This expression will generate all angles coterminal with 240 degrees.

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Answer: Last one

Step-by-step explanation:

The largest angle is [tex]\frac{7a}{4}[/tex] and the smallest angle is [tex]\frac{3a}{4}[/tex].

In this case, we have the angles [tex]\frac{5a}{2}, \frac{3a}{4}, and \frac{7a}{4}[/tex]. So we can set up the equation:

[tex]\frac{5a}{2} + \frac{3a}{4} + \frac{7a}{4} = 180[/tex]

To solve for "a", we can simplify the left side of the equation by finding a common denominator:

[tex]\frac{(10a + 3a + 7a)}{4} = 180[/tex]

Simplifying the left side gives:

[tex]\frac{20a}{4} = 180[/tex]

And further simplifying gives:

5a = 180

Dividing both sides by 5 gives:

a = 36

Now that we know the value of "a", we can substitute it back into each angle expression to find their actual values:

[tex]\frac{5a}{2} = \frac{5(36)}{2} = \frac{903a}{4} = \frac{3(36)}{4} = \frac{277a}{4} = \frac{7(36)}{4} = 63[/tex]

Therefore, [tex]\frac{7a}{4} = 63[/tex] is the largest angle and [tex]\frac{3a}{4} = 27[/tex] is the smallest angle.

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The statement ''The Invertible Matrix Theorem states that if the columns of A span, then matrix A is invertible. Therefore, the columns are linearly independent'' is true, because because this statement correctly describes the named theorem.

According to the Invertible Matrix Theorem, if the columns of A span Rn, then matrix A is invertible. This also means that the columns of A are linearly independent. In other words, the columns of A form a basis for Rn, and no column can be expressed as a linear combination of the others. Therefore, the statement is true.

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The measure of angle x is 70°.

Here we have the image of some triangles, and we want to find the value of the interior angle x in the left triangle.

What you need to remember here is that the sum of the interior angles of any triangle is always equal to 180°.

Then, for the left triangle, we can write:

30° + 80° + x° = 180°

Now we can solve that equation for x, then we will get:

x° = 180° - 80° - 30°

x = 70°

That is the measure of angle x.

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The value of the function (f·g)(-9) is 186.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions f(x)=2x²-4x-15 and g(x)=x+12.

Here, (f·g)(x)=f(x)+g(x)

= 2x²-4x-15+x+12

= 2x²-3x-3

(f·g)(-9)=2(-9)²-3(-9)-3

= 2×81+27-3

= 162+27-3

= 162+24

= 186

Therefore, the value of (f·g)(-9) is 186.

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By trigonometric formulas, there are two solution sets for the trigonometric equation 2 · cos β = - √(3 · cos β) + sin β + 2 · cos β: β₁ ≈ 0.402π + 2π · k, β₂ = - 0.402π - 2π · k, where k is an integer.

In this problem we find the case of a trigonometric equation, whose roots must be found by algebra properties and trigonometric formulas. First, write the complete expression:

2 · cos β = - √(3 · cos β) + sin β + 2 · cos β

Second, simplify the expression by algebra properties:

√(3 · cos β) = sin β

Third, square both sides and simplify the expression:

3 · cos β = sin² β

3 · cos β = 1 - cos² β

cos² β + 3 · cos β - 1

Fourth, factor the resulting expression:

(cos β - 0.303) · (cos β + 3.303)

Fifth, determine the set of solutions:

cos β = 0.303

β₁ ≈ 0.402π + 2π · k, β₂ = - 0.402π - 2π · k, where k is an integer.

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The actual distance between City C and City D is 4,224,000 feet.

What is total distance?

Whole distance refers to the actual travel distance between the origin and destination locations of the item.

We can use the given scale to convert the distance between City A and City B to feet:

500 miles = 500 * 5280 feet = 2,640,000 feet

Since 1.6 feet represents this distance on the wall map, we have:

1.6 feet = 2,640,000 feet / x

where x is the actual distance represented by 1.6 feet on the map. Solving for x, we get:

x = 2,640,000 feet / 1.6 feet = 1,650,000 feet per foot

Therefore, the  total distance between City C and City D, which is 2.56 feet on the map, corresponds to:

2.56 feet * 1,650,000 feet per foot = 4,224,000 feet

So the actual distance between City C and City D is 4,224,000 feet.

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Answer:

こんにちは

Step-by-step explanation:

2. 答えは2.5

次の番号 3 の場合は 6.9 次の番号は 4 の場合は 5.6

43. g(6) = 5602.33

44. f(5) = 61.

The exponential function is defined by the equation:g(x) = 31​(7)x − 2So, we need to evaluate the function g(x) at x = 6. Then, g(6) is given by;g(6) = 31​(7)6 − 2= 31​(7)4= 16807/3Thus, g(6) = 5602.33 (rounded to two decimal places).Similarly, the exponential function is defined by the equation:f(x) = 4(2)x − 1 − 2We need to evaluate the function f(x) at x = 5. Then, f(5) is given by;f(5) = 4(2)5 − 1 − 2= 4(16) − 1 − 2= 64 − 1 − 2= 61Thus, f(5) = 61.

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The total amount of money two friends had is $3430.

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Here the ratio of the money of friends = 4:3.

Let us take shares of money as 4x and 3x.

Here larger amount  4x=R1960

=> 4x=1960

=> x= 1960/4= $490

Then Total amount = 4x+3x=7x

=> Total amount = 7*490=$3430

Hence the total amount of money two friends had is $3430.

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Use the rule, “add 8” to find the cost of 6 T-shirts. The cost of the T-shirt is $48.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.

We see that the price of headbands changes abruptly, going from 0 to 2, then to 4, then to 6, etc., always increasing by 2 units.

The “add 8” rule applies to the price of T-shirts because each one costs $8.

In order to determine the cost of six headbands, we then perform the following calculations:

8 + 8 + 8 + 8 + 8 + 8 = 6 x 8 = $48

We see that we can easily multiply the required quantity of T-shirts by the cost per unit of T-shirts.

Therefore, the cost of the T-shirt is $48.

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The question is incomplete, the complete question is given below:

The school store sells headbands for $2 each and T-shirts for$8 each. Write ordered pairs to compare the cost of headbands to T-shirts for 0,1,2,3,4, and 5 of each item.

Cost of Headbands ($)

0

2

4

6

8

10

​

Cost of T-shirts ($)

8

16

24

32

40

Ordered Pairs

(0, 0)

(2, 8)

(4, 16)

(6, 24)

(8, 32)

(10, 40)

​

To make the solid figure true using column A and column B are as follow,

1.ice cube → cube

2.tissue roll → cylinder

3.match box →rectangular prism

4.volleyball →sphere

5.can of sardines →cylinder

6.milk box → rectangular prism

7.volcano →cone

8.toblerone →triangular prism

9.bus→rectangular prism

10.roof of a nipa hut→ triangular pyramid

Solid figure represents the following shape,

1. Ice cube represents the cube shape as all the sides are of same length.

2. Tissue roll represents the cylindrical shape.

3. Match box is an perfect example for rectangular prism.

4. Volleyball represents the spherical shape.

5. Can of sardines is one of the perfect example of cylinder.

6. Milk box is also one of the example of rectangular prism

7.volcano represents the cone.

8.toblerone is representing triangular prism.

9.bus is a example of rectangular prism

10.roof of a nipa hut it is an example of triangular pyramid

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The above question is incomplete, the complete question is:

Choose the solid figure in Column B to make each statement is true of column A.

Column A.

1.ice cube

2.tissue roll

3.match box

4.volleyball

5.can of sardines

6.milk box

7.volcano

8.toblerone

9.bus

10.roof of a nipa hut

Column B.

A. cone

B. cube

C. cylinder

D. rectangular prism

E. sphere

F. square pyramid

G. triangular prism

H. triangular pyramid​

The present value of the land is $52,337.28

The worth of an anticipated revenue stream assessed as of the valuation date is known as a present value in the fields of economics and finance.

There are different kinds of PV models including:

How to solve:

We use the formula:

Present value of land= $18,000 + (2,000 * 17.1684)= $52,337.28

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Answer:

Step-by-step explanation:

Angles in a quadrilateral add to 360°. So

[tex]60+80+120+x=360[/tex]   (where [tex]x[/tex] is the fourth angle)

[tex]260+x=360[/tex]  

[tex]x=100[/tex]°    (after subtracted 260 from both sides of equation)

Answer:

Your answer is <PBD = 56

Step-by-step explanation:

That red square indicate that its a right triangle meaning that <PBH is 90°

Those two angle <PBD and <DBH are complementary angle meaning that those two angle add up to 90°

So,

<PBD + <DBH = 90°

(3k + 65°) + 34 = 90

3k + 65 + 34 = 90

3k = -9

k = -3

Plug in k = -3 in <PBD to solve for the measure angle.

<PBD = (3k + 65°) ; k = -3

<PBD = 3(-3) + 65

<PBD = -9 + 65

<PBD = 56

When one holder has a height of 5 inches and a width of 4 inches, this is approximately have Surface Area of 1385.44  inches² if we round to two decimal places.

what is surface area ?

Surface area is a measurement of the overall space occupied by an object's surface. It is the total area of the object's faces, sides, and curved sections. The surface area of a cube, for instance, is equal to the total of the areas of each of its six square faces. Similar to a sphere, a cylinder's surface area is equal to the total of the areas of its two circular bases and its curved surface. Units of surface area include square inches (in²), square feet (ft²), and square metres (m²). It is a crucial measurement in a variety of industries, including science, engineering, and building.

given

We must first determine the cylinder's surface area in order to determine how much material will be required to create one cylindrical pencil case.

The following is the calculation for a cylinder's surface area:

S = 2πrh + 2πr²

S stands for surface area.

r is the cylinder's radius.

h is the cylinder's height.

The radius of the holder is equal to half of its 4 inch circumference, or 2 inches.

Consequently, the total area for one holder will be:

S = 2π(2)(5) + 2π(2)²

S = 20π

In order to create one pencil holder, Mrs. Howard would require 20 square inches of material.

She would require: to create pencil holders for each of her 22 pupils.

22 × 20 inches of material equals 440  inches².

When one holder has a height of 5 inches and a width of 4 inches, this is approximately 1385.44  inches² if we round to two decimal places.

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